;;;; solve-triangle.lisp
(defpackage #:solve-triangle
  (:use :cl)
  (:export #:solve-asa
           #:solve-ssa))

(in-package #:solve-triangle)

;; SAA, ASA -- Law of Sines
;; SSA -- Law of Sines, (or 0 1 2) solutions
;; SAS -- Law of Cosines
;; SSS -- Law of Cosines

(defun solve-asa (anglea sidea angleb)
  "Solve a ASA triangle using the method of sines.  Angles assumed to be in degrees."
  (let* ((anglec (- 180 anglea angleb))
         (sideb (/ (* (sin angleb)
                      sidea)
                   (sin anglea)))
         (sidec (/ (* (sin anglec)
                      sidea)
                   (sin anglea))))
    (list :angle-a anglea
          :angle-b angleb
          :angle-c anglec
          :side-a sidea
          :side-b sideb
          :side-c sidec)))

(defun solve-ssa (sidea sideb anglea)
  "Solve an SSA triangle using the method of sines.  Angles are assumed to be in degrees."
  (let ((angleb (asin (/ (* sideb (sin anglea))
                         sidea))))
    (cond
      ((< 1 angleb) nil)
      (())))
  (let* ((angleb (asin (/ (* sideb (sin anglea))
                          sidea)))
         (anglec (- 180 anglea angleb))
         (sidec (/ (* (sin anglec)
                      sidea)
                   (sin anglea))))
    (list :angle-a anglea
          :angle-b angleb
          :angle-c anglec
          :side-a sidea
          :side-b sideb
          :side-c sidec)))